Book contents
- Frontmatter
- Preface
- Contents
- Part 1 Student Thinking
- 1a Foundations for Beginning Calculus
- 1 On Developing a Rich Conception of Variable
- 2 Rethinking Change
- 3 Foundational Reasoning Abilities that Promote Coherence in Students' Function Understanding
- 4 The Concept of Accumulation in Calculus
- 1b Infinity, Limit and Divisibility
- 5 Developing Notions of Infinity
- 6 Layers of Abstraction: Theory and Design for the Instruction of Limit Concepts
- 7 Divisibility and Transparency of Number Representations
- 1c Proving Theorems
- 8 Overcoming Students' Difficulties in Learning to Understand and Construct Proofs
- 9 Mathematical Induction: Cognitive and Instructional Considerations
- 10 Proving Starting from Informal Notions of Symmetry and Transformations
- 11 Teaching and Learning Group Theory
- 12 Teaching for Understanding: A Case of Students' Learning to Use the Uniqueness Theorem as a Tool in Differential Equations
- Part 2 Cross-Cutting Themes
- About the Editors
This chapter is part of a book that is no longer available to purchase from Cambridge Core
4 - The Concept of Accumulation in Calculus
from 1a - Foundations for Beginning Calculus
Book contents
- Frontmatter
- Preface
- Contents
- Part 1 Student Thinking
- 1a Foundations for Beginning Calculus
- 1 On Developing a Rich Conception of Variable
- 2 Rethinking Change
- 3 Foundational Reasoning Abilities that Promote Coherence in Students' Function Understanding
- 4 The Concept of Accumulation in Calculus
- 1b Infinity, Limit and Divisibility
- 5 Developing Notions of Infinity
- 6 Layers of Abstraction: Theory and Design for the Instruction of Limit Concepts
- 7 Divisibility and Transparency of Number Representations
- 1c Proving Theorems
- 8 Overcoming Students' Difficulties in Learning to Understand and Construct Proofs
- 9 Mathematical Induction: Cognitive and Instructional Considerations
- 10 Proving Starting from Informal Notions of Symmetry and Transformations
- 11 Teaching and Learning Group Theory
- 12 Teaching for Understanding: A Case of Students' Learning to Use the Uniqueness Theorem as a Tool in Differential Equations
- Part 2 Cross-Cutting Themes
- About the Editors
Summary
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- Information
- Making the ConnectionResearch and Teaching in Undergraduate Mathematics Education, pp. 43 - 52Publisher: Mathematical Association of AmericaPrint publication year: 2008
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